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 A342093 Primes that can be represented as (1/2)*Sum_{i=0..m} binomial(m,i)*prime(i+k) for some k and m >= 2. 1

%I #27 Feb 28 2021 20:48:33

%S 47,61,73,103,137,157,167,179,223,257,263,337,347,383,467,563,613,719,

%T 733,757,769,877,887,1021,1097,1223,1297,1327,1367,1453,1481,1571,

%U 1613,1621,1759,1811,1987,1997,2003,2027,2039,2129,2251,2473,2477,2539,2593,2633,2767,2879,3001,3037,3083,3119

%N Primes that can be represented as (1/2)*Sum_{i=0..m} binomial(m,i)*prime(i+k) for some k and m >= 2.

%C Each prime is just listed once, though it may arise in more than one way.

%H Robert Israel, <a href="/A342093/b342093.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 73 is a term because it is prime and Sum_{i=0..2} binomial(2,i)*prime(11+i) = 31+2*37+41 = 2*73.

%e a(10) = 257 arises in two ways:

%e 2*257 = Sum_{i=0..3} binomial(3,i)*prime(17+i) = 59+3*61+3*67+71

%e and Sum_{i=0..4} binomial(4,i)*prime(9+i) = 23+4*29+6*31+4*37+41.

%p N:= 10^4: # for terms <= N

%p S:= {}:

%p for m from 2 do

%p for k from 2 do

%p v:= add(binomial(m,i)*ithprime(i+k),i=0..m)/2;

%p if v > N then break fi;

%p if isprime(v) then

%p S:= S union {v}; count:= count+1;

%p fi;

%p od;

%p if k = 2 then break fi

%p od:

%p sort(convert(S,list));

%Y Contains A338273.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Feb 28 2021

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Last modified September 10 17:45 EDT 2024. Contains 375792 sequences. (Running on oeis4.)